Step 1 Clean the crabs if the fishmonger didn't do so. Using scissors, cut off 1/4 inch from below the eyes. Turn the crabs over and lift the apron, the small piece that comes up from the bottom of the shell, and remove. Turn over, and open the top shell from each side and remove the gills. Rinse and pat dry.
Step 2 Whisk the yolk in a bowl until fluffy. Whisk in the lemon juice, then add 1/2 teaspoon of salt, then whisk in the garlic. Slowly drizzle in the oil. Refrigerate the aioli until ready to use.
Step 3Mix the flour, Old Bay seasoning, the remaining 1/2 teaspoon of salt and pepper to taste in a shallow dish. Lightly dredge the crabs in the mixture.
Step 4Melt the butter in a skillet over medium-high heat. Add the crabs and cook until they've turned pink, about 3 to 4 minutes, then turn and cook another 3 to 4 minutes.
Step 5Meanwhile, toast the bread. Place 1 slice on each of 4 plates. Spread lightly with the aioli. Place a lettuce leaf and tomato slice on top of each slice. Place a crab on top of each sandwich, then add 1 tablespoon of aioli to each. Use the remaining aioli for another use, or pass at the table.